Wendy hailed Perry as "an extraordinary man", and also thanked his children - Sophie, 18, and Jack, 21, who he had with ex-wife Rachel Sharp - for their support.
She said: "The past 11 years with Luke were the happiest years of my life, and I am grateful to have had that time with him.
"I also want to thank his children, family, and friends for their love and support. We have found comfort in one another and in the knowledge that our lives were touched by an extraordinary man. He will be dearly missed."
Meanwhile, Sophie recently discussed her father's passing in an Instagram post.
She wrote: "A lot has happened in this past week for me. Everything is happening so fast. I made it back from Malawi just in time to be here with my family, and in the past 24 hours I have received an overwhelming amount of love and support.
"I cannot individually respond to the hundreds of beautiful and heartfelt messages, but I see them, and appreciate you all for sending positivity to my family and I. (sic)"